Deleting Numbers

题意翻译

这是一道交互题。 已知 $n$, 有一个未知数 $x$ $(1\le x\le n)$，你需要求出 $x$ 的值。 一开始，你有一个集合 $S=\{x|x\le n,x\in \mathbb{N^+}\}$，你可以对这个集合执行不超过 $10000$ 次 A、B、C 操作（总和不超过）。 A: A $a$，表示求出 $S$ 中 $a$ 的倍数的个数 $(1\le a\le n)$ B: B $a$，表示求出 $S$ 中 $a$ 的倍数的个数并将这些 $a$ 的倍数从 $S$ 中删去（$x$ 是不会被删掉的） $(2\le a\le n)$ C: C $a$，表示你知道了 $x=a$ $(1\le a\le n)$ 所有的 $a$ 均为整数。

题目描述

This is an interactive problem. There is an unknown integer $ x $ ( $ 1\le x\le n $ ). You want to find $ x $ . At first, you have a set of integers $ \{1, 2, \ldots, n\} $ . You can perform the following operations no more than $ 10000 $ times: - A $ a $ : find how many numbers are multiples of $ a $ in the current set. - B $ a $ : find how many numbers are multiples of $ a $ in this set, and then delete all multiples of $ a $ , but $ x $ will never be deleted (even if it is a multiple of $ a $ ). In this operation, $ a $ must be greater than $ 1 $ . - C $ a $ : it means that you know that $ x=a $ . This operation can be only performed once. Remember that in the operation of type B $ a>1 $ must hold. Write a program, that will find the value of $ x $ .

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 1\le n\le 10^5 $ ). The remaining parts of the input will be given throughout the interaction process.

输出格式

In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer $ a $ ( $ 1\le a\le n $ for operations A and C, $ 2\le a\le n $ for operation B). This line desribes operation you make. If your operation has type C your program should terminate immediately. Else your program should read one line containing a single integer, which is the answer to your operation. After outputting each line, don't forget to flush the output. To do it use: - fflush(stdout) in C/C++; - System.out.flush() in Java; - sys.stdout.flush() in Python; - flush(output) in Pascal; - See the documentation for other languages. It is guaranteed, that the number $ x $ is fixed and won't change during the interaction process. Hacks: To make a hack, use such input format: The only line should contain two integers $ n $ , $ x $ ( $ 1 \leq x \leq n \leq 10^5 $ ).

输入输出样例

输入样例 #1

10

2

4

0

输出样例 #1

B 4

A 2

A 8

C 4

说明

Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process. In the first test $ n=10 $ and $ x=4 $ . Initially the set is: $ \{1,2,3,4,5,6,7,8,9,10\} $ . In the first operation, you ask how many numbers are multiples of $ 4 $ and delete them. The answer is $ 2 $ because there are two numbers divisible by $ 4 $ : $ \{4,8\} $ . $ 8 $ will be deleted but $ 4 $ won't, because the number $ x $ will never be deleted. Now the set is $ \{1,2,3,4,5,6,7,9,10\} $ . In the second operation, you ask how many numbers are multiples of $ 2 $ . The answer is $ 4 $ because there are four numbers divisible by $ 2 $ : $ \{2,4,6,10\} $ . In the third operation, you ask how many numbers are multiples of $ 8 $ . The answer is $ 0 $ because there isn't any number divisible by $ 8 $ in the current set. In the fourth operation, you know that $ x=4 $ , which is the right answer.

题意翻译

这是一道交互题。 已知 $n$, 有一个未知数 $x$ $(1\le x\le n)$，你需要求出 $x$ 的值。 一开始，你有一个集合 $S=\{x|x\le n,x\in \mathbb{N^+}\}$，你可以对这个集合执行不超过 $10000$ 次 A、B、C 操作（总和不超过）。 A: A $a$，表示求出 $S$ 中 $a$ 的倍数的个数 $(1\le a\le n)$ B: B $a$，表示求出 $S$ 中 $a$ 的倍数的个数并将这些 $a$ 的倍数从 $S$ 中删去（$x$ 是不会被删掉的） $(2\le a\le n)$ C: C $a$，表示你知道了 $x=a$ $(1\le a\le n)$ 所有的 $a$ 均为整数。